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<div align="center"><big> <b><big><br>
</big></b></big></div>
<div align="center"><big><b><big>Welcome to the 2022 Spring
talks of ODTU-Bilkent Algebraic Geometry Seminars</big></b></big><b><br>
</b><b> </b><b> </b></div>
<b> </b>
<div align="center"><i>since 2000</i><br>
<b> </b> </div>
<div align="center"><b> </b><b> </b><b><b>=================================================================</b>
</b><br>
<b> </b><br>
This week the <a
href="http://www.bilkent.edu.tr/%7Esertoz/agseminar.htm"
target="_blank" moz-do-not-send="true">ODTU-Bilkent
Algebraic Geometry Seminar</a> is <b>Online.</b> <br>
<br>
<i><font color="#ff00ff">This talk will begin at <u><b>15:40</b></u><u>
(GMT+3)</u></font></i><br>
<br>
<b>=================================================================</b></div>
<div align="center"><br>
<br>
<div align="center"><b><img
src="cid:part1.HZEPDJq2.mm9ogVpZ@bilkent.edu.tr" alt=""
class="" width="400" height="299"> </b><font size="-1"><i>
</i></font></div>
Georgi Petrov<br>
Return to the past<br>
<font size="2"><i>(from the artist's homepage)</i></font><br>
<div align="left"> <b><b><font color="#ff0000">Speaker:<font
color="#000000"> Alexander Degtyarev<br>
</font></font></b></b></div>
<div align="left"><b><b><font color="#ff0000">Affiliation:<font
color="#000000"> Bilkent</font><br>
Title:<font color="#000000"> Towards 800 conics on a
smooth quartic surfaces<br>
</font><br>
</font></b></b></div>
</div>
<div align="left"><b><b><font color="#ff0000">Abstract:</font></b></b><font
color="#ff0000"><font color="#000000"> This will be a
technical talk where I will discuss a few computational
aspects of my work in progress towards the following
conjecture.<br>
<br>
Conjecture: A smooth quartic surface in P3 may contain at
most 800 conics.<br>
<br>
I will suggest and compare several arithmetical reductions
of the problem. Then, for the chosen one, I will discuss a
few preliminary combinatorial bounds and some techniques
used to handle the few cases where those bounds are not
sufficient.<br>
<br>
At the moment, I am quite confident that the conjecture
holds. However, I am trying to find all smooth quartics
containing 720 or more conics, in the hope to find the
real quartic maximizing the number of real lines and to
settle yet another conjecture (recall that we count all
conics, both irreducible and reducible).<br>
<br>
Conjecture: If a smooth quartic X⊂P3 contains more than
720 conics, then X has no lines; in particular, all conics
are irreducible.<br>
<br>
Currently, similar bounds are known only for sextic
K3-surfaces in P4.<br>
<br>
As a by-product, I have found a few examples of large
configurations of conics that are not Barth--Bauer, i.e.,
do not contain<br>
a 16-tuple of pairwise disjoint conics or, equivalently,
are not Kummer surfaces with all 16 Kummer divisors
conics.<i><br>
</i><i> </i><br>
</font></font></div>
<div align="left"><font color="#ff0000"><font color="#000000"><b><font
color="#ff0000">Date:<font color="#000000"> 11 March
2022</font></font></b>, Friday</font></font><br>
</div>
<div align="left"><font color="#ff0000"><font color="#000000"><b>
<font color="#ff0000">Time: </font>15:40 <i>(GMT+3)</i></b><br>
<b><font color="#ff0000">Place: </font></b><font
color="#ff0000"><font color="#000000"><b>Zoom<br>
</b></font></font></font></font></div>
<div align="left"><font color="#ff0000"><font color="#000000"><font
color="#ff0000"><font color="#000000"><b><br>
</b></font></font></font></font></div>
<blockquote>
<p><font color="#ff0000"><font color="#000000"><font
color="#ff0000"><font color="#000000"><b><b
style="color:rgb(51,51,51);font-family:arial,verdana,sans-serif;font-size:14px">One
day before the seminar, an announcement with the
Zoom meeting link will be sent to those who
registered with Sertöz. <br>
</b></b></font></font></font></font></p>
<p><font color="#ff0000"><font color="#000000"><font
color="#ff0000"><font color="#000000"><b><b
style="color:rgb(51,51,51);font-family:arial,verdana,sans-serif;font-size:14px">If
you have registered before for one of the
previous talks, there is no need to register
again; you will automatically receive a link for
this talk too.<br>
</b></b></font></font></font></font></p>
<p><font color="#ff0000"><font color="#000000"><font
color="#ff0000"><font color="#000000"><b><b
style="color:rgb(51,51,51);font-family:arial,verdana,sans-serif;font-size:14px">If
you have not registered before, please contact
him at <a
href="mailto:sertoz@bilkent.edu.tr?subject=Zoom%20Seminar%20Address%20Request"
moz-do-not-send="true">sertoz@bilkent.edu.tr</a>.</b></b></font></font></font></font></p>
</blockquote>
<p><font color="#ff0000"><font color="#000000"><font
color="#ff0000"><font color="#000000"><b> </b></font></font></font></font></p>
<div align="left"><br>
</div>
<div align="left">Please bring your own tea and cookies and
self-serve at the convenience of your own home! 😁<span
class="gmail-moz-smiley-s1"></span></div>
<div align="left"><br>
</div>
<div align="left">You are most cordially invited to attend.</div>
<div align="left"><br>
</div>
<div align="left">Ali Sinan Sertöz<br>
<font color="#ff0000"><font color="#000000"><b><font
color="#ff0000"> </font></b></font></font></div>
<pre class="gmail-moz-signature" cols="72">----------------------------------------------------------------------------
Ali Sinan Sertöz
Bilkent University, Department of Mathematics, 06800 Ankara, Turkey
Office: (90)-(312) - 290 1490
Department: (90)-(312) - 266 4377
Fax: (90)-(312) - 290 1797
e-mail: <a class="gmail-moz-txt-link-abbreviated moz-txt-link-freetext" href="mailto:sertoz@bilkent.edu.tr" moz-do-not-send="true">sertoz@bilkent.edu.tr</a>
Web: <a href="http://sertoz.bilkent.edu.tr" moz-do-not-send="true">sertoz.bilkent.edu.tr</a>
----------------------------------------------------------------------------</pre>
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